Abstract : The p-version of the finite element method is a new, important, computationally efficient, approach to finite element analysis. It is more robust than the conventional h-version and its rate of convergence, for domains with corners and for other singularity problems, is twice that of the h-version. Hierarchic elements which implement the p-version efficiently have been formulated so as to enforce C superscript 0 or C superscript 1 continuity in the planar case, and so as to enforce C superscript 0 continuity in three dimensions. Recent research accomplishments include: 1. Development of an algorithm that finds all roots of an analytic function in a finite domain. 2. Preprocessing procedures to restrict the search in unbounded domains which contain roots to bounded domains. 3. A reliable numerical argument principle algorithm to compute number of zeros within a closed contour. 4. Formulation of equations which determine the nature of stress singularity at a corner of a plate composed of n isotropic materials. All of the above are used in the extraction method for p-version finite element analysis of composite materials with corners.